Dynamics of an SI epidemic model with external effects in a polluted environment |
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Authors: | Bing Liu Ying Duan |
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Institution: | a Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114007, PR Chinab Fushun Sifang Senior High School, Fushun 113122, PR Chinac Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, PR China |
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Abstract: | In a polluted environment, considering the biological population infected with some kinds of diseases and hunted by human beings, we formulate two SI pollution-epidemic models with continuous and impulsive external effects, respectively, and investigate the dynamics of such systems. We assume that only the susceptible population is hunted by human beings. For the continuous system, we obtain sufficient conditions of the ultimate boundedness of solutions and the global asymptotical stability of equilibria. For the impulsive system, by using the comparison theorem and the analysis method, we show that under different conditions the disease-free periodic solution is globally asymptotically attractive, or the system is permanent. Numerical simulations confirm our theoretical results. |
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Keywords: | Pollution-epidemic model Impulsive pollution input Global asymptotical stability Extinction Permanence |
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